
# import packages
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns

from sklearn.model_selection import ShuffleSplit, GridSearchCV
from sklearn.ensemble import RandomForestClassifier, RandomForestRegressor
from sklearn.preprocessing import StandardScaler, OneHotEncoder, MinMaxScaler
from sklearn.pipeline import Pipeline
from sklearn.compose import ColumnTransformer
from sklearn.cluster import KMeans
from sklearn.manifold import TSNE

import plotly.express as px

from sklearn.decomposition import PCA
from sklearn.inspection import permutation_importance
from sklearn.cluster import AgglomerativeClustering 
from sklearn.metrics import silhouette_samples, silhouette_score, homogeneity_score, completeness_score, v_measure_score, adjusted_rand_score, adjusted_mutual_info_score, fowlkes_mallows_score
from scipy.cluster import hierarchy 
from scipy.spatial import distance_matrix 
from sklearn.cluster import DBSCAN 

import matplotlib.cm as cm


# read data
data = pd.read_csv("./Absenteeism_at_work.csv", sep=';', index_col="ID")
data


data.head()


data.tail()


data.shape

(740, 20)


# data types
data.info()

<class 'pandas.core.frame.DataFrame'>
Int64Index: 740 entries, 11 to 35
Data columns (total 20 columns):
 #   Column                           Non-Null Count  Dtype  
---  ------                           --------------  -----  
 0   Reason for absence               740 non-null    int64  
 1   Month of absence                 740 non-null    int64  
 2   Day of the week                  740 non-null    int64  
 3   Seasons                          740 non-null    int64  
 4   Transportation expense           740 non-null    int64  
 5   Distance from Residence to Work  740 non-null    int64  
 6   Service time                     740 non-null    int64  
 7   Age                              740 non-null    int64  
 8   Work load Average/day            740 non-null    float64
 9   Hit target                       740 non-null    int64  
 10  Disciplinary failure             740 non-null    int64  
 11  Education                        740 non-null    int64  
 12  Son                              740 non-null    int64  
 13  Social drinker                   740 non-null    int64  
 14  Social smoker                    740 non-null    int64  
 15  Pet                              740 non-null    int64  
 16  Weight                           740 non-null    int64  
 17  Height                           740 non-null    int64  
 18  Body mass index                  740 non-null    int64  
 19  Absenteeism time in hours        740 non-null    int64  
dtypes: float64(1), int64(19)
memory usage: 121.4 KB


# min and max values
data.describe()


data.isnull().sum()

Reason for absence                 0
Month of absence                   0
Day of the week                    0
Seasons                            0
Transportation expense             0
Distance from Residence to Work    0
Service time                       0
Age                                0
Work load Average/day              0
Hit target                         0
Disciplinary failure               0
Education                          0
Son                                0
Social drinker                     0
Social smoker                      0
Pet                                0
Weight                             0
Height                             0
Body mass index                    0
Absenteeism time in hours          0
dtype: int64


# divide columns to numerical and categorical ones
categorical_atts = ['Reason for absence','Month of absence','Day of the week',
                     'Seasons','Disciplinary failure', 'Education', 'Social drinker',
                     'Social smoker', 'Pet', 'Son']
numerical_atts = data.drop(columns=categorical_atts).columns.to_list()


# number of unique values in categorical atts
data[categorical_atts].nunique()

Reason for absence      28
Month of absence        13
Day of the week          5
Seasons                  4
Disciplinary failure     2
Education                4
Social drinker           2
Social smoker            2
Pet                      6
Son                      5
dtype: int64


# plot distribution of "reason for absence" column
sns.set_style("whitegrid")
sns.catplot(data=data, x='Reason for absence', kind= 'count',size=4, aspect=4, palette='muted')

C:\Users\gruha\miniconda3\envs\ash_off\lib\site-packages\seaborn\categorical.py:3750: UserWarning: The `size` parameter has been renamed to `height`; please update your code.
  warnings.warn(msg, UserWarning)

<seaborn.axisgrid.FacetGrid at 0x257d8d58e50>


# plot distribution of numerical attributes
num_df = data[numerical_atts]
plt.figure(figsize=(20,20))
for i in range(1, 11):
    plt.subplot(4, 3, i)
    sns.distplot(num_df[num_df.columns[i-1]],bins=14)

C:\Users\gruha\miniconda3\envs\ash_off\lib\site-packages\seaborn\distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
  warnings.warn(msg, FutureWarning)
C:\Users\gruha\miniconda3\envs\ash_off\lib\site-packages\seaborn\distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
  warnings.warn(msg, FutureWarning)
C:\Users\gruha\miniconda3\envs\ash_off\lib\site-packages\seaborn\distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
  warnings.warn(msg, FutureWarning)
C:\Users\gruha\miniconda3\envs\ash_off\lib\site-packages\seaborn\distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
  warnings.warn(msg, FutureWarning)
C:\Users\gruha\miniconda3\envs\ash_off\lib\site-packages\seaborn\distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
  warnings.warn(msg, FutureWarning)
C:\Users\gruha\miniconda3\envs\ash_off\lib\site-packages\seaborn\distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
  warnings.warn(msg, FutureWarning)
C:\Users\gruha\miniconda3\envs\ash_off\lib\site-packages\seaborn\distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
  warnings.warn(msg, FutureWarning)
C:\Users\gruha\miniconda3\envs\ash_off\lib\site-packages\seaborn\distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
  warnings.warn(msg, FutureWarning)
C:\Users\gruha\miniconda3\envs\ash_off\lib\site-packages\seaborn\distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
  warnings.warn(msg, FutureWarning)
C:\Users\gruha\miniconda3\envs\ash_off\lib\site-packages\seaborn\distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
  warnings.warn(msg, FutureWarning)


# correlation matrix
num_corr = num_df.corr()
plt.figure(figsize=(10,6))
sns.heatmap(num_corr, annot=True, fmt=".3f",vmin=-1, vmax=1, linewidths=.5, cmap = sns.color_palette("RdBu", 100))
plt.yticks(rotation=0)
plt.show()


# display boxlots
plt.figure(figsize=(8,8))
sns.boxplot(x="variable", y="value", data=pd.melt(num_df))
plt.xticks(rotation=90)
plt.show()


# Check for outliers using boxplots and drop them
for num_att in numerical_atts:
    # Getting 75 and 25 percentile of variable "i"
    Q3, Q1 = np.percentile(data[num_att], [75,25])
    MEAN = data[num_att].mean()
    
    # Calculating Interquartile range
    IQR = Q3 - Q1
    
    # Calculating upper extream and lower extream
    minimum = Q1 - (IQR*1.5)
    maximum = Q3 + (IQR*1.5)
    
    # Replacing all the outliers value to Mean
    data_clean=data.drop(data.loc[data[num_att]< minimum,num_att].index) 
    data_clean=data.drop(data.loc[data[num_att]> maximum,num_att].index)


# size reduced to 150 from 740
len(data_clean)

150


# transform data
numeric_transformer = MinMaxScaler()
#categorical_transformer = OneHotEncoder(sparse=False, handle_unknown='ignore')

# exclude target attr,bute
numerical_atts = [x for x in numerical_atts if x not in ['Absenteeism time in hours']]
preprocessor = ColumnTransformer(
    transformers=[
        ('num', numeric_transformer, numerical_atts),
        ('cat', 'passthrough', categorical_atts)
    ], remainder='passthrough')
data_pp = preprocessor.fit_transform(data_clean)


# X, y splitting (we dont need train test splitting since this model is just for feature importances)
y_original = data_pp[:,-1].reshape(-1, 1)
y = np.round(MinMaxScaler((0,2)).fit_transform(y_original)).ravel()
X = np.delete(data_pp,-1,1) 

# cross-validation with 10 splits
cross_val = ShuffleSplit(n_splits=10, random_state = 42)

# define model
rf = RandomForestClassifier(random_state = 0,max_features=None,n_jobs=-1)

# parameters 
parameters = {  
                "n_estimators":[1000],
                #'max_depth': list(range(1,11)),
                #"criterion": ["gini","entropy"],
                #"criterion": ["mse","mae"],
                #"class_weight": [None, "balanced"],
                #"max_features":["auto", None, "log2"],
                }

# grid search for parameters
grid = GridSearchCV(estimator=rf, param_grid=parameters, cv=cross_val, n_jobs=-1)#multithreading; all cores are used
grid.fit(X,y)

# print best scores
print("The best parameters are %s with a score of %0.2f"
      % (grid.best_params_, grid.best_score_))

The best parameters are {'n_estimators': 1000} with a score of 0.71


# pie-chart 
atts = numerical_atts+categorical_atts
plt.figure(figsize=(10,10))
plt.pie(grid.best_estimator_.feature_importances_, labels=atts, shadow=True, startangle=90)

([<matplotlib.patches.Wedge at 0x25803eccc40>,
  <matplotlib.patches.Wedge at 0x25803ecc3d0>,
  <matplotlib.patches.Wedge at 0x25803f3b280>,
  <matplotlib.patches.Wedge at 0x25803f3b9d0>,
  <matplotlib.patches.Wedge at 0x25803f45160>,
  <matplotlib.patches.Wedge at 0x25803f458b0>,
  <matplotlib.patches.Wedge at 0x25803f51040>,
  <matplotlib.patches.Wedge at 0x25803f51790>,
  <matplotlib.patches.Wedge at 0x25803f51ee0>,
  <matplotlib.patches.Wedge at 0x25803f61670>,
  <matplotlib.patches.Wedge at 0x25803eccaf0>,
  <matplotlib.patches.Wedge at 0x25803f6d520>,
  <matplotlib.patches.Wedge at 0x25803f6dc70>,
  <matplotlib.patches.Wedge at 0x25803f7c400>,
  <matplotlib.patches.Wedge at 0x25803f7cb50>,
  <matplotlib.patches.Wedge at 0x25803f872e0>,
  <matplotlib.patches.Wedge at 0x25803f87a30>,
  <matplotlib.patches.Wedge at 0x25803f951c0>,
  <matplotlib.patches.Wedge at 0x25803f95910>],
 [Text(-0.1313317603092574, 1.0921318458565668, 'Transportation expense'),
  Text(-0.35811278919022577, 1.0400746272351793, 'Distance from Residence to Work'),
  Text(-0.5948118899952959, 0.9253101185657835, 'Service time'),
  Text(-0.841352203173818, 0.7086088273614454, 'Age'),
  Text(-1.0786359856128447, 0.2157415364296074, 'Work load Average/day '),
  Text(-1.0277641991974853, -0.39204687327914256, 'Hit target'),
  Text(-0.8823203448169655, -0.6568948234855191, 'Weight'),
  Text(-0.7636115970775396, -0.7917684818232471, 'Height'),
  Text(-0.5050656456950577, -0.9771942967182292, 'Body mass index'),
  Text(0.714035788870899, -0.836751392118061, 'Reason for absence'),
  Text(1.0497860254680054, 0.32855638896860406, 'Month of absence'),
  Text(0.8285710971126086, 0.7235122231376664, 'Day of the week'),
  Text(0.5455915771294705, 0.955159584030531, 'Seasons'),
  Text(0.4305774190125454, 1.0122267958498703, 'Disciplinary failure'),
  Text(0.376445491938291, 1.033580568508976, 'Education'),
  Text(0.30857437518300984, 1.0558323043838047, 'Social drinker'),
  Text(0.2572882981820978, 1.06948713485416, 'Social smoker'),
  Text(0.173647801443996, 1.0862073655861788, 'Pet'),
  Text(0.05227897673389785, 1.0987569834097333, 'Son')])


# permutation importance with RF classifier
atts_arr = np.array(atts)
result = permutation_importance(grid, X, y, n_repeats=10,
                                random_state=42, n_jobs=-1)
sorted_idx = result.importances_mean.argsort()

fig, ax = plt.subplots()
ax.boxplot(result.importances[sorted_idx].T,
           vert=False, labels=atts_arr[sorted_idx])
ax.set_title("Permutation Importances (train set)")
fig.tight_layout()
plt.show()

for i in result.importances_mean.argsort()[::-1]:
     print(f"{atts_arr[i]:<8} "
           f"{result.importances_mean[i]:.3f}"
           f" +/- {result.importances_std[i]:.3f}")

Reason for absence 0.305 +/- 0.021
Day of the week 0.049 +/- 0.013
Work load Average/day  0.035 +/- 0.009
Body mass index 0.033 +/- 0.007
Hit target 0.021 +/- 0.006
Seasons  0.009 +/- 0.004
Month of absence 0.007 +/- 0.002
Transportation expense 0.007 +/- 0.000
Age      0.003 +/- 0.003
Disciplinary failure 0.000 +/- 0.000
Pet      0.000 +/- 0.000
Education 0.000 +/- 0.000
Height   0.000 +/- 0.000
Weight   0.000 +/- 0.000
Social drinker 0.000 +/- 0.000
Social smoker 0.000 +/- 0.000
Service time 0.000 +/- 0.000
Distance from Residence to Work 0.000 +/- 0.000
Son      0.000 +/- 0.000


# select important attributes
selected_atts = ['Reason for absence', 'Day of the week', 'Work load Average/day','Body mass index','Hit target', 
                     'Seasons', 'Month of absence', 'Transportation expense', 'Age']

selected_atts_idx=np.where(np.isin(atts,selected_atts))[0]
X_selected = X[:,selected_atts_idx]


# run k-means for range of 10 clusters then analyse with elbow method
clusters = []

for i in range(1, 11):
    km = KMeans(n_clusters=i).fit(X_selected)
    clusters.append(km.inertia_)
    
fig, ax = plt.subplots(figsize=(12, 8))
sns.lineplot(x=list(range(1, 11)), y=clusters, ax=ax)
ax.set_title('Searching for Elbow')
ax.set_xlabel('Clusters')
ax.set_ylabel('Inertia')

# Annotate arrow
ax.annotate('Possible Elbow Point', xy=(4, clusters[3]), xytext=(4, clusters[3]+1000), xycoords='data',          
             arrowprops=dict(arrowstyle='->', connectionstyle='arc3', color='blue', lw=2))

ax.annotate('Possible Elbow Point', xy=(3,clusters[2] ), xytext=(3, clusters[2]+1000), xycoords='data',          
             arrowprops=dict(arrowstyle='->', connectionstyle='arc3', color='blue', lw=2))

ax.annotate('Possible Elbow Point', xy=(2,clusters[1] ), xytext=(2, clusters[1]+1000), xycoords='data',          
             arrowprops=dict(arrowstyle='->', connectionstyle='arc3', color='blue', lw=2))

plt.show()


# 2 clusters
km2 = KMeans(n_clusters=2).fit(X_selected)

# plot using tsne 
X_embedded  = TSNE(n_components=3, perplexity=10, random_state=24).fit_transform( X_selected )
colors = np.array([x for x in 'bgrcmykbgrcmykbgrcmykbgrcmyk'])

fig = px.scatter_3d(x=X_embedded [:,0],y=X_embedded [:,1],z=X_embedded [:,2],color=colors[km2.labels_])
fig.show()

C:\Users\gruha\miniconda3\envs\ash_off\lib\site-packages\sklearn\manifold\_t_sne.py:780: FutureWarning: The default initialization in TSNE will change from 'random' to 'pca' in 1.2.
  warnings.warn(
C:\Users\gruha\miniconda3\envs\ash_off\lib\site-packages\sklearn\manifold\_t_sne.py:790: FutureWarning: The default learning rate in TSNE will change from 200.0 to 'auto' in 1.2.
  warnings.warn(


# 3 clusters
km3 = KMeans(n_clusters=3).fit(X_selected)

# plot using tsne 
X_embedded  = TSNE(n_components=3, perplexity=10,random_state=24).fit_transform( X_selected )

fig = px.scatter_3d(x=X_embedded [:,0],y=X_embedded [:,1],z=X_embedded [:,2],color=colors[km3.labels_])
fig.show()

C:\Users\gruha\miniconda3\envs\ash_off\lib\site-packages\sklearn\manifold\_t_sne.py:780: FutureWarning:

The default initialization in TSNE will change from 'random' to 'pca' in 1.2.

C:\Users\gruha\miniconda3\envs\ash_off\lib\site-packages\sklearn\manifold\_t_sne.py:790: FutureWarning:

The default learning rate in TSNE will change from 200.0 to 'auto' in 1.2.


# 4 clusters
km4 = KMeans(n_clusters=4).fit(X_selected)

# plot using tsne 
X_embedded  = TSNE(n_components=3, perplexity=10,random_state=24).fit_transform( X_selected )

fig = px.scatter_3d(x=X_embedded [:,0],y=X_embedded [:,1],z=X_embedded [:,2],color=colors[km4.labels_])
fig.show()

C:\Users\gruha\miniconda3\envs\ash_off\lib\site-packages\sklearn\manifold\_t_sne.py:780: FutureWarning:

The default initialization in TSNE will change from 'random' to 'pca' in 1.2.

C:\Users\gruha\miniconda3\envs\ash_off\lib\site-packages\sklearn\manifold\_t_sne.py:790: FutureWarning:

The default learning rate in TSNE will change from 200.0 to 'auto' in 1.2.


# PCA for reducing dimensions to 3
pca = PCA(n_components=3)
pca_results = pca.fit_transform(X_selected)

# running k-means on resuts of pca
km_pca = KMeans(n_clusters=3).fit(pca_results)
fig = px.scatter_3d(x=pca_results [:,0],y=pca_results [:,1],z=pca_results [:,2],color=colors[km_pca.labels_])
fig.show()


# define a function to plot silhouette values of clusters
def silhouette_plot(X, y, n_clusters, ax=None):
    if ax is None:
        ax = plt.gca()

    # Compute the silhouette scores for each sample
    silhouette_avg = silhouette_score(X, y)
    sample_silhouette_values = silhouette_samples(X, y)

    y_lower = padding = 2
    for i in range(n_clusters):
        # Aggregate the silhouette scores for samples belonging to
        ith_cluster_silhouette_values = sample_silhouette_values[y == i]
        ith_cluster_silhouette_values.sort()

        size_cluster_i = ith_cluster_silhouette_values.shape[0]
        y_upper = y_lower + size_cluster_i

        color = cm.nipy_spectral(float(i) / n_clusters)
        ax.fill_betweenx(np.arange(y_lower, y_upper),
                         0,
                         ith_cluster_silhouette_values,
                         facecolor=color,
                         edgecolor=color,
                         alpha=0.7)

        # Label the silhouette plots with their cluster numbers at the middle
        ax.text(-0.05, y_lower + 0.5 * size_cluster_i, str(i + 1))

        # Compute the new y_lower for next plot
        y_lower = y_upper + padding

    ax.set_xlabel("The silhouette coefficient values")
    ax.set_ylabel("Cluster label")

    # The vertical line for average silhoutte score of all the values
    ax.axvline(x=silhouette_avg, c='r', alpha=0.8, lw=0.8, ls='-')
    ax.annotate('Average',
                xytext=(silhouette_avg, y_lower * 1.025),
                xy=(0, 0),
                ha='center',
                alpha=0.8,
                c='r')

    ax.set_yticks([])  # Clear the yaxis labels / ticks
    ax.set_xticks([0, 0.2, 0.4, 0.6, 0.8, 1])
    ax.set_ylim(0, y_upper + 1)
    ax.set_xlim(-0.075, 1.0)
    return ax


# plot silhouette coefficients
plt.figure(figsize=(20,30))
for i in range(2,11):  
    agnes = AgglomerativeClustering(n_clusters=i, linkage='average')
    agnes_labels = agnes.fit_predict(X_selected)
    plt.subplot(5,2,i-1)
    silhouette_plot(X_selected,agnes_labels,i)


# 6 clusters
agnes6 = AgglomerativeClustering(n_clusters=6, linkage='average').fit(X_selected)

# plot using tsne 
X_embedded  = TSNE(n_components=3, perplexity=10,random_state=24).fit_transform( X_selected )

fig = px.scatter_3d(x=X_embedded [:,0],y=X_embedded [:,1],z=X_embedded [:,2],color=colors[agnes6.labels_])
fig.show()

C:\Users\gruha\miniconda3\envs\ash_off\lib\site-packages\sklearn\manifold\_t_sne.py:780: FutureWarning:

The default initialization in TSNE will change from 'random' to 'pca' in 1.2.

C:\Users\gruha\miniconda3\envs\ash_off\lib\site-packages\sklearn\manifold\_t_sne.py:790: FutureWarning:

The default learning rate in TSNE will change from 200.0 to 'auto' in 1.2.


# there's no inertia in attribute of AgglomerativeClustering class so we use scipy's distance matrix
dist = distance_matrix(X_selected, X_selected)

# dendrogram
Z = hierarchy.linkage(dist, 'average')
plt.figure(figsize=(18, 15))
dendro = hierarchy.dendrogram(Z, leaf_rotation=0, leaf_font_size=12, orientation='right')

C:\Users\gruha\AppData\Local\Temp/ipykernel_8120/742401282.py:5: ClusterWarning:

scipy.cluster: The symmetric non-negative hollow observation matrix looks suspiciously like an uncondensed distance matrix


# search for best parameters by using silhouette_score
score_list=[]
for eps in np.arange(0.5,20,0.5):
    for min_samples in range(3,20):
        db = DBSCAN(eps=eps, min_samples=min_samples).fit(X_selected)
        labels = db.labels_
        n = len(np.unique(labels))
        if n>1:
            score=silhouette_score(X_selected, labels)
            score_list.append((score,(eps,min_samples)))
     
biggest_score = sorted(score_list)[-1]  
best_eps, best_min_spamles = biggest_score[1]
best_eps, best_min_spamles

(5.0, 11)


# best model for DBSCAN
db_best = DBSCAN(eps=best_eps, min_samples=best_min_spamles).fit(X_selected)

# plot using tsne 
X_embedded  = TSNE(n_components=3, perplexity=10,random_state=24).fit_transform( X_selected )

fig = px.scatter_3d(x=X_embedded [:,0],y=X_embedded [:,1],z=X_embedded [:,2],color=colors[db_best.labels_])
fig.show()

C:\Users\gruha\miniconda3\envs\ash_off\lib\site-packages\sklearn\manifold\_t_sne.py:780: FutureWarning:

The default initialization in TSNE will change from 'random' to 'pca' in 1.2.

C:\Users\gruha\miniconda3\envs\ash_off\lib\site-packages\sklearn\manifold\_t_sne.py:790: FutureWarning:

The default learning rate in TSNE will change from 200.0 to 'auto' in 1.2.


# print metric for chosen models
models = [km4, km_pca, agnes6, db_best] 
names = ["K-MEANS:","PCA + K-MEANS:","AGNES:", "DBSCAN:"]

for i, model in enumerate(models):
    labels = model.labels_
    n = len(np.unique(labels))
    y = np.round(MinMaxScaler((0,n)).fit_transform(y_original)).ravel()
    # Number of clusters in labels, ignoring noise if present.
    n_clusters_ = len(set(labels)) - (1 if -1 in labels else 0)
    n_noise_ = list(labels).count(-1)
    print(names[i])
    print('Estimated number of clusters: %d' % n_clusters_)
    print('Estimated number of noise points: %d' % n_noise_)
    print("Homogeneity: %0.3f" % homogeneity_score(y, labels))
    print("Completeness: %0.3f" % completeness_score(y, labels))
    print("V-measure: %0.3f" % v_measure_score(y, labels))
    print("Adjusted Rand Index: %0.3f"
          % adjusted_rand_score(y, labels))
    print("Adjusted Mutual Information: %0.3f"
          % adjusted_mutual_info_score(y, labels))
    print("Fowlkes-Mallows score: %0.3f"
          % fowlkes_mallows_score(y, labels))
    print("Silhouette Coefficient: %0.3f"
          % silhouette_score(X, labels))
    print("\n")

K-MEANS:
Estimated number of clusters: 4
Estimated number of noise points: 0
Homogeneity: 0.157
Completeness: 0.133
V-measure: 0.144
Adjusted Rand Index: 0.075
Adjusted Mutual Information: 0.121
Fowlkes-Mallows score: 0.344
Silhouette Coefficient: 0.330


PCA + K-MEANS:
Estimated number of clusters: 3
Estimated number of noise points: 0
Homogeneity: 0.147
Completeness: 0.176
V-measure: 0.160
Adjusted Rand Index: 0.077
Adjusted Mutual Information: 0.143
Fowlkes-Mallows score: 0.423
Silhouette Coefficient: 0.437


AGNES:
Estimated number of clusters: 6
Estimated number of noise points: 0
Homogeneity: 0.211
Completeness: 0.188
V-measure: 0.199
Adjusted Rand Index: 0.110
Adjusted Mutual Information: 0.156
Fowlkes-Mallows score: 0.348
Silhouette Coefficient: 0.276


DBSCAN:
Estimated number of clusters: 2
Estimated number of noise points: 0
Homogeneity: 0.029
Completeness: 0.045
V-measure: 0.035
Adjusted Rand Index: -0.035
Adjusted Mutual Information: 0.024
Fowlkes-Mallows score: 0.557
Silhouette Coefficient: 0.518

	Reason for absence	Month of absence	Day of the week	Seasons	Transportation expense	Distance from Residence to Work	Service time	Age	Work load Average/day	Hit target	Disciplinary failure	Education	Son	Social drinker	Social smoker	Pet	Weight	Height	Body mass index	Absenteeism time in hours
count	740.000000	740.000000	740.000000	740.000000	740.000000	740.000000	740.000000	740.000000	740.000000	740.000000	740.000000	740.000000	740.000000	740.000000	740.000000	740.000000	740.000000	740.000000	740.000000	740.000000
mean	19.216216	6.324324	3.914865	2.544595	221.329730	29.631081	12.554054	36.450000	271.490235	94.587838	0.054054	1.291892	1.018919	0.567568	0.072973	0.745946	79.035135	172.114865	26.677027	6.924324
std	8.433406	3.436287	1.421675	1.111831	66.952223	14.836788	4.384873	6.478772	39.058116	3.779313	0.226277	0.673238	1.098489	0.495749	0.260268	1.318258	12.883211	6.034995	4.285452	13.330998
min	0.000000	0.000000	2.000000	1.000000	118.000000	5.000000	1.000000	27.000000	205.917000	81.000000	0.000000	1.000000	0.000000	0.000000	0.000000	0.000000	56.000000	163.000000	19.000000	0.000000
25%	13.000000	3.000000	3.000000	2.000000	179.000000	16.000000	9.000000	31.000000	244.387000	93.000000	0.000000	1.000000	0.000000	0.000000	0.000000	0.000000	69.000000	169.000000	24.000000	2.000000
50%	23.000000	6.000000	4.000000	3.000000	225.000000	26.000000	13.000000	37.000000	264.249000	95.000000	0.000000	1.000000	1.000000	1.000000	0.000000	0.000000	83.000000	170.000000	25.000000	3.000000
75%	26.000000	9.000000	5.000000	4.000000	260.000000	50.000000	16.000000	40.000000	294.217000	97.000000	0.000000	1.000000	2.000000	1.000000	0.000000	1.000000	89.000000	172.000000	31.000000	8.000000
max	28.000000	12.000000	6.000000	4.000000	388.000000	52.000000	29.000000	58.000000	378.884000	100.000000	1.000000	4.000000	4.000000	1.000000	1.000000	8.000000	108.000000	196.000000	38.000000	120.000000

Unsupervised learning¶

Assignment 2¶

1. Data Exploration¶

2. Data Visualization¶

3. Outlier Detection¶

NORMALIZATION¶

4. Feature Selection¶

5. Clustering¶

6. Evaluation Metrics¶

	Reason for absence	Month of absence	Day of the week	Seasons	Transportation expense	Distance from Residence to Work	Service time	Age	Work load Average/day	Hit target	Disciplinary failure	Education	Son	Social drinker	Social smoker	Pet	Weight	Height	Body mass index	Absenteeism time in hours
ID
11	26	7	3	1	289	36	13	33	239.554	97	0	1	2	1	0	1	90	172	30	4
36	0	7	3	1	118	13	18	50	239.554	97	1	1	1	1	0	0	98	178	31	0
3	23	7	4	1	179	51	18	38	239.554	97	0	1	0	1	0	0	89	170	31	2
7	7	7	5	1	279	5	14	39	239.554	97	0	1	2	1	1	0	68	168	24	4
11	23	7	5	1	289	36	13	33	239.554	97	0	1	2	1	0	1	90	172	30	2
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
11	14	7	3	1	289	36	13	33	264.604	93	0	1	2	1	0	1	90	172	30	8
1	11	7	3	1	235	11	14	37	264.604	93	0	3	1	0	0	1	88	172	29	4
4	0	0	3	1	118	14	13	40	271.219	95	0	1	1	1	0	8	98	170	34	0
8	0	0	4	2	231	35	14	39	271.219	95	0	1	2	1	0	2	100	170	35	0
35	0	0	6	3	179	45	14	53	271.219	95	0	1	1	0	0	1	77	175	25	0